Question: What's the first wrong statement in the proof below that $ \triangle BDE \cong \triangle BCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle CFE \cong \angle DBE$ $, \ $ $ \overline{EF} \cong \overline{BE}$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ $ \overline{AB} \cong \overline{BE}$ $, \ $ $ \angle BAC \cong \angle BED$ $, \ $ and $\ $ $ \angle ACB \cong \angle BDE$ Proof $ \triangle BDE \cong \triangle FCE$ because ASA $ \overline{DE} \cong \overline{CE}$ because corresponding parts of congruent triangles are congruent $ \overline{BE} \cong \overline{DF}$ because corresponding parts of congruent triangles are congruent $ \angle BDE \cong \angle ECF$ because corresponding parts of congruent triangles are congruent $ \triangle BDE \cong \triangle BCA$ because AAS $ \triangle BDE \cong \triangle BCE$ because SSS
Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \overline{DF} \cong \overline{BE}$ is the first wrong statement.